I have tried Custom Options: Out come was that every time you choose a size it zeroed out the price automatically. The correct price up in the shopping cart, but on the product page when you select a size the price changes to 0.00
Concerning that statement. I guess that must be you set some special setting for option or set price mark-up.
What I can offer you to do. Try to delete this product with which you have issues. Next create one test simple product manually and add to it a couple of sizes and check if the issue remains.
The situation you face is the not correct, since the price of custom options should be added to general product price.
I have tried Adding a Attribute (I could be doing this wrong for sizes): The attribute shows up on the backend, which makes me select a size for every shirt. Pointless. I want this to only show up on the site. I shouldn’t be choosing a size for a shirt, because then the buyer can not pick the size.
If I understood you correctly, you have created attribute with drop-down type. It is used as drop-down with selection mainly for configurable products. In you use this attribute with simple product, you can select only one of options (it won’t be drop-down at the front-end). Here is the article on configurable products for you to get the idea -
P.S. Configurable products make sense in case you need to track inventory of sizes. Otherwise it will take too much time and efforts to use them.